Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917850446299136 |
|---|---|
| author | Fisher, David Lafont, Jean-François Miller, Nicholas Stover, Matthew |
| author_facet | Fisher, David Lafont, Jean-François Miller, Nicholas Stover, Matthew |
| contents | We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces. In higher codimension, we prove finiteness for geodesic submanifolds of dimension at least $2$ that are maximal, i.e., not properly contained in a proper geodesic submanifold of the ambient $n$-manifold. The proof is a mix of structure theory for arithmetic groups, dynamics, and geometry in negative curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_04619 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids Fisher, David Lafont, Jean-François Miller, Nicholas Stover, Matthew Geometric Topology Differential Geometry Dynamical Systems Group Theory We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces. In higher codimension, we prove finiteness for geodesic submanifolds of dimension at least $2$ that are maximal, i.e., not properly contained in a proper geodesic submanifold of the ambient $n$-manifold. The proof is a mix of structure theory for arithmetic groups, dynamics, and geometry in negative curvature. |
| title | Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids |
| topic | Geometric Topology Differential Geometry Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/1802.04619 |